Prove that sin(x)+sin(y)=2sin((x+y)/2)cos((x-y)/2)
We know that 1. sin(a+b) = sin(a)cos(b)+sin(b)cos(a) and 2. sin(a-b) = sin(a)cos(b)-sin(b)cos(a) Add equations 1. and 2. sin(a+b)+sin(a-b) = 2sin(a)cos(b)+sin(b)cos(a)-sin(b)cos(a) = 2sin(a)cos(b) Let x=a+b and y=a-b, hence x+y=2a so a=(x+y)/2 and x-y=2b so b=(x-y)/2 Therefoe sin(x)+sin(y) = 2sin((x+y)/2)cos((x-y)/2)
AV
Related Maths A Level answers
All answers ▸(Core 2) Show that the region bounded by the curve y = 7x+ 6 - (1/x^2), the x axis and the lines x = 1 and x = 2 equals 16
What is the indefinite integral ∫5exp(3-4x)dx ?
The Curve C has equation y = 3x^4 - 8x^3 - 3. Find dy/dx.
Differentiate with respect to x, x^2*e^(tan(x))